When you're peeing and a fart has developed. You try to hold it in, but when you finally are forced to let it go, the resulting release of pressure makes your pee stream get stronger, sending pee onto the underside of the toilet lid. Akin to the recoil of a rifle, hence the term "peecoil".

Andrea: How the hell do you manage to get pee on the underside of the toilet lid?

David: Those burritos I had last night gave me gas, and the peecoil from a huge fart is what's responsible for the peed-on toilet seat.

Andrea: Kinda like a rifle, huh? Well, it looks like a rifle you have there in your hand.